# What does it mean for a set to be bounded?

1. Oct 26, 2009

### royzizzle

what does it mean for a set to be bounded??

in the context of the hein-borel theorem

i mean the mathematically rigorous definition

2. Oct 27, 2009

### Office_Shredder

Staff Emeritus
Re: what does it mean for a set to be bounded??

S a subset of Rn is bounded if there exists M>0 so that for all x in S, |x|<M

3. Oct 27, 2009

### Moo Of Doom

Re: what does it mean for a set to be bounded??

Another equivalent definition is that it has finite diameter, where

$$\mathrm{diam}(S) = \sup_{x, y \in S}(\mathrm{dist}(x, y)).$$

This is applicable to any metric space (though the Heine-Borel theorem is not!).